Solve m-4/0-1*m-1/0-3=-1

$$\frac { m - 4 } { 0 - 1 } \times \frac { m - 1 } { 0 - 3 } = - 1$$

Solve for m

$$m=\frac{5+\sqrt{3}i}{2}\approx 2.5+0.866025404i$$

$$m=\frac{-\sqrt{3}i+5}{2}\approx 2.5-0.866025404i$$

Steps Using the Quadratic Formula

Subtract 1 from 0 to get -1.

$$\frac{m-4}{-1}\times \frac{m-1}{0-3}=-1$$

Anything divided by -1 gives its opposite. To find the opposite of m-4, find the opposite of each term.

$$\left(-m-\left(-4\right)\right)\times \frac{m-1}{0-3}=-1$$

Subtract 3 from 0 to get -3.

$$\left(-m-\left(-4\right)\right)\times \frac{m-1}{-3}=-1$$

Multiply both numerator and denominator by -1.

$$\left(-m-\left(-4\right)\right)\times \frac{-m+1}{3}=-1$$

Express \left(-m-\left(-4\right)\right)\times \frac{-m+1}{3} as a single fraction.

$$\frac{\left(-m-\left(-4\right)\right)\left(-m+1\right)}{3}=-1$$

The opposite of -4 is 4.

$$\frac{\left(-m+4\right)\left(-m+1\right)}{3}=-1$$

Add 1 to both sides.

$$\frac{\left(-m+4\right)\left(-m+1\right)}{3}+1=0$$

Apply the distributive property by multiplying each term of -m+4 by each term of -m+1.

$$\frac{m^{2}-m-4m+4}{3}+1=0$$

Combine -m and -4m to get -5m.

$$\frac{m^{2}-5m+4}{3}+1=0$$

Divide each term of m^{2}-5m+4 by 3 to get \frac{1}{3}m^{2}-\frac{5}{3}m+\frac{4}{3}.

$$\frac{1}{3}m^{2}-\frac{5}{3}m+\frac{4}{3}+1=0$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{3}m^{2}-\frac{5}{3}m+\frac{4}{3}+\frac{3}{3}=0$$

Since \frac{4}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}m^{2}-\frac{5}{3}m+\frac{4+3}{3}=0$$

Add 4 and 3 to get 7.

$$\frac{1}{3}m^{2}-\frac{5}{3}m+\frac{7}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{3} for a, -\frac{5}{3} for b, and \frac{7}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-\frac{5}{3}\right)±\sqrt{\left(-\frac{5}{3}\right)^{2}-4\times \frac{1}{3}\times \frac{7}{3}}}{2\times \frac{1}{3}}$$

Square -\frac{5}{3} by squaring both the numerator and the denominator of the fraction.

$$m=\frac{-\left(-\frac{5}{3}\right)±\sqrt{\frac{25}{9}-4\times \frac{1}{3}\times \frac{7}{3}}}{2\times \frac{1}{3}}$$

Multiply -4 times \frac{1}{3}.

$$m=\frac{-\left(-\frac{5}{3}\right)±\sqrt{\frac{25}{9}-\frac{4}{3}\times \frac{7}{3}}}{2\times \frac{1}{3}}$$

Multiply -\frac{4}{3} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$m=\frac{-\left(-\frac{5}{3}\right)±\sqrt{\frac{25-28}{9}}}{2\times \frac{1}{3}}$$

Add \frac{25}{9} to -\frac{28}{9} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$m=\frac{-\left(-\frac{5}{3}\right)±\sqrt{-\frac{1}{3}}}{2\times \frac{1}{3}}$$

Take the square root of -\frac{1}{3}.

$$m=\frac{-\left(-\frac{5}{3}\right)±\frac{\sqrt{3}i}{3}}{2\times \frac{1}{3}}$$

The opposite of -\frac{5}{3} is \frac{5}{3}.

$$m=\frac{\frac{5}{3}±\frac{\sqrt{3}i}{3}}{2\times \frac{1}{3}}$$

Multiply 2 times \frac{1}{3}.

$$m=\frac{\frac{5}{3}±\frac{\sqrt{3}i}{3}}{\frac{2}{3}}$$

Now solve the equation m=\frac{\frac{5}{3}±\frac{\sqrt{3}i}{3}}{\frac{2}{3}} when ± is plus. Add \frac{5}{3} to \frac{i\sqrt{3}}{3}.

$$m=\frac{5+\sqrt{3}i}{\frac{2}{3}\times 3}$$

Divide \frac{5+i\sqrt{3}}{3} by \frac{2}{3} by multiplying \frac{5+i\sqrt{3}}{3} by the reciprocal of \frac{2}{3}.

$$m=\frac{5+\sqrt{3}i}{2}$$

Now solve the equation m=\frac{\frac{5}{3}±\frac{\sqrt{3}i}{3}}{\frac{2}{3}} when ± is minus. Subtract \frac{i\sqrt{3}}{3} from \frac{5}{3}.

$$m=\frac{-\sqrt{3}i+5}{\frac{2}{3}\times 3}$$

Divide \frac{5-i\sqrt{3}}{3} by \frac{2}{3} by multiplying \frac{5-i\sqrt{3}}{3} by the reciprocal of \frac{2}{3}.

$$m=\frac{-\sqrt{3}i+5}{2}$$

The equation is now solved.

$$m=\frac{5+\sqrt{3}i}{2} m=\frac{-\sqrt{3}i+5}{2}$$

Steps for Completing the Square

Subtract 1 from 0 to get -1.

$$\frac{m-4}{-1}\times \frac{m-1}{0-3}=-1$$

Anything divided by -1 gives its opposite. To find the opposite of m-4, find the opposite of each term.

$$\left(-m-\left(-4\right)\right)\times \frac{m-1}{0-3}=-1$$

Subtract 3 from 0 to get -3.

$$\left(-m-\left(-4\right)\right)\times \frac{m-1}{-3}=-1$$

Multiply both numerator and denominator by -1.

$$\left(-m-\left(-4\right)\right)\times \frac{-m+1}{3}=-1$$

Express \left(-m-\left(-4\right)\right)\times \frac{-m+1}{3} as a single fraction.

$$\frac{\left(-m-\left(-4\right)\right)\left(-m+1\right)}{3}=-1$$

The opposite of -4 is 4.

$$\frac{\left(-m+4\right)\left(-m+1\right)}{3}=-1$$

Multiply both sides by 3.

$$\left(-m+4\right)\left(-m+1\right)=-3$$

Apply the distributive property by multiplying each term of -m+4 by each term of -m+1.

$$m^{2}-m-4m+4=-3$$

Combine -m and -4m to get -5m.

$$m^{2}-5m+4=-3$$

Subtract 4 from both sides.

$$m^{2}-5m=-3-4$$

Subtract 4 from -3 to get -7.

$$m^{2}-5m=-7$$

Divide -5, the coefficient of the x term, by 2 to get -\frac{5}{2}. Then add the square of -\frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-5m+\left(-\frac{5}{2}\right)^{2}=-7+\left(-\frac{5}{2}\right)^{2}$$

Square -\frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-5m+\frac{25}{4}=-7+\frac{25}{4}$$

Add -7 to \frac{25}{4}.

$$m^{2}-5m+\frac{25}{4}=-\frac{3}{4}$$

Factor m^{2}-5m+\frac{25}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{5}{2}\right)^{2}=-\frac{3}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{5}{2}\right)^{2}}=\sqrt{-\frac{3}{4}}$$

Simplify.

$$m-\frac{5}{2}=\frac{\sqrt{3}i}{2} m-\frac{5}{2}=-\frac{\sqrt{3}i}{2}$$

Add \frac{5}{2} to both sides of the equation.

$$m=\frac{5+\sqrt{3}i}{2} m=\frac{-\sqrt{3}i+5}{2}$$